Ira H. Shavel

Abstract

This paper is concerned with a
class of algebraic surfaces of general type constructed from indefinite division
quaternion algebras whose centers are totally real number fields. These surfaces are
quotients of the product of two upper half planes by Fuchsian groups obtained from
the unit groups of maximal orders of such algebras. In the case where the field is real
quadratic, we give smoothness conditions for the resulting surfaces and list all
smooth surfaces of geometric genus 0. Finally, we give a lower bound for the torsion
part of H2(Z).